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- # Innlevering 2
-
- ## A2
-
- ### 1
-
- A) \mmatrix{4&1} \mmatrix{3&0 \\ 2&7} = \mmatrix{4 * 3 + 1 * 2 & 4 * 0 + 1 * 0} = \mmatrix{14 & 0}
-
- B) \mmatrix{1&1 \\ 1&1} \mmatrix{2&2 \\ 2&2} = \mmatrix{1 * 2 + 1 * 2 & 1 * 2 + 1 * 2 \\ 1 * 2 + 1 * 2 & 1 * 2 + 1 * 2} = \mmatrix{4 & 4 \\ 4 & 4}
-
- C) \mmatrix{2&3&1 \\ 4&8&2} \mmatrix{5&1 \\ 1&0 \\ 3&2} = \mmatrix{2 * 5+3 * 1 + 1 * 3 & 2 * 1 + 3 * 0 + 1 * 2 \\ 4 * 5 + 8 * 1 + 2 * 3 & 4 * 1 + 8 * 0 + 2 * 2} = \mmatrix{16 & 4 \\ 34 & 8}
-
- D) \mmatrix{4&5 \\ 2&1 \\ 1&-1 \\ 3&7} \mmatrix{2&1&3&0 \\ 4&1&2&1} = \mmatrix{
- 4 * 2 + 5 * 4 & 4 * 1 + 5 * 1 & 4 * 3 + 5 * 2 & 4 * 0 + 5 * 1 \\
- 2 * 2 + 1 * 4 & 2 * 1 + 1 * 1 & 2 * 3 + 1 * 2 & 2 * 0 + 1 * 1 \\
- 1 * 2 + (-1 * 4) & 1 * 1 + (-1 * 1) & 1 * 3 + (-1 * 2) & 1 * 0 + (-1 * 1) \\
- 3 * 2 + 7 * 4 & 3 * 1 + 7 * 1 & 3 * 3 + 7 * 3 & 3 * 0 + 7 * 1
- } = \mmatrix{
- 28 & 9 & 22 & 5 \\
- 8 & 3 & 8 & 1 \\
- -2 & 0 & 1 & -1 \\
- 34 & 10 & 30 & 7
- }
-
- ### 2
-
- * A = \mmatrix{4&0 \\ 2&3 \\ 6&1}
- * B = \mmatrix{3&1 \\ 7&2}
- * C = \mmatrix{8&3&2 \\ 5&0&1 \\ 6&6&7}
- * D = \mmatrix{0&1&5 \\ 2&4&2}
- * E = \mmatrix{9&1&2 \\ 0&4&4 \\ 5&0&7}
-
- \pagebreak
-
- A)
- * A: 2x3
- * B: 2x2
- * C: 3x3
- * D: 3x2
- * E: 3x3
-
- B)
- 1) AB: Udefinert, fordi 3 != 2
- 2) AB + C: Udefinert, fordi AB er udefinert
- 3) 3E: Definert, fordi skalarprodukt er alltid definert
- 4) DA - B: Udefinert, fordi DA er en 3x3-matrise og B er en 2x2-matrise
- 5) BD + A: Udefinert, fordi BD er udefinert
- 6) ABD + 2CE: Udefinert, fordi AB er udefinert
-
- ### 12
-
- A) det \mmatrix{1&0 \\ 0&1} = 1 * 1 - 0 * 0 = 1
-
- B) det \mmatrix{15&2 \\ 0&8} = 15 * 8 - 0 * 2 = 120
-
- C) det \mmatrix{
- 2 & 0 & 0 \\
- 1 & 3 & 4 \\
- 1 & 4 & 2
- } = 2 det \mmatrix{
- 3 & 4 \\
- 4 & 3
- } - 0 det \mmatrix{
- 1 & 4 \\
- 4 & 2
- } + 0 det \mmatrix{
- 3 & 4 \\
- 4 & 2
- } =
- 2(3 * 3 - 4 * 4) - 0 + 0 = 2(9 * 16) = 2 * 144 = 288
-
- D) det \mmatrix{30&2 \\ -40&4} = 120 - (-80) = 200
-
- ### 13
-
- A) det \mmatrix{3&5 \\ -2&4} = 12 - (-10) = 22
- B) det \mmatrix{-5&6 \\ -7&-2} = 10 - (-42) = 52
- C) det \mmatrix{
- -2 & 1 & 4 \\
- 3 & 5 & -7 \\
- 1 & 6 & 2
- } = -2 det \mmatrix{
- 5 & -7 \\
- 6 & 2
- } - 1 \mmatrix{
- 3 & -7 \\
- 1 & 2
- } + 4 \mmatrix{
- 3 & 5 \\
- 1 & 6
- } =
- -2(5 * 2 - 6 * -7) - 1(3 * 2 - 1 * -7) + 4(3 * 6 - 1 * 5) = 104 - 13 + 52 = 143
-
- ## B1
-
- ### 5
-
- * A = \mmatrix{
- 2 & -3 & 1 \\
- -1 & 2 & 4 \\
- 1 & 3 & -1
- }
-
- 1) A^2 = \mmatrix{2&-3&1 \\ -1&2&4 \\ 1&3&-1} \mmatrix{2&-3&1 \\ -1&2&4 \\ 1&3&-1} = \mmatrix{
- 2 * 2 + -3 * -1 + 1 * 1 &
- }
-
- ### 6
-
- ### 7
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